Generally, separators with nanofiber layers are widely known (for example, refer to Patent document 1). Compared to separators with typical fiber layers, in the case of the separators with nanofiber layers, fibers are thin and pores are fine and uniform, so that insulation and dendrite resistance are superior. Therefore, it is possible that, with high insulation and high dendrite resistance, the thickness of the separator is reduced and the ion conductivity thereof is thus enhanced. Furthermore, the porosity of the separators with nanofiber layers is larger than that of the separators with typical fiber layers. Thus, the separators with nanofiber layers have high electrolyte sustainability, thereby further increasing the ion conductivity. As such, the separators with nanofiber layers can have high insulation, high dendrite resistance and high ion conductivity. Such a separator can be suitably used in a battery (including a primary battery and a secondary battery) or a condenser (referred to as a capacitor). Furthermore, in the present invention, the term “nanofiber” refers to a fiber, an average diameter of which ranges from several nanometers to several thousand nanometers.